Gelfand and Kolmogorov numbers of Sobolev embeddings of weighted function spaces II

We consider the Gelfand and Kolmogorov numbers of compact embeddings between weighted function spaces of Besov and Triebel-Lizorkin type with polynomial weights in the non-limiting case. Our main purpose here is to complement our previous results in \cite{ZF10} in the context of the quasi-Banach setting, $0<p,q\le \mathrm{\infty }$. In addition, sharp estimates for their approximation numbers in several cases left open in Skrzypczak (JAT, 2005) are provided.